Hey all, I'm on that top list at number 15 right now (was num 8 when i got the 0:53.897

) using the wheel. I'll have to look at the specifics of the tuning, but honestly it's not very special. It's all about smashing into the corners as other people said.
My car was The Honda Integra w/ racing mods and all other upgrades possible, but NO turbo. This gave it somewhere around 300HP that was tuned down to 295. I think I had the front at maximum downforce. Also the max speed was tuned down a bit to about 143mph i think. With 143 you should hit max speed right before you need to "brake" into the first turn. I had the 1st place ghost time to race against and it was pretty much even.
I haven't tried the celica, though I have it. I tried a racing modified '97 civic which has about 100kg less weight than the integra, but it wasn't as good. Plus i like the integra (have an rsx type-s myself) which is why I even tried the TT originally.
The real trick is tapping the handbrake right before smashing the wall on the first turn. This puts you in the correct direction to accel out. The first place time has a ridiculous first turn which is why his is so much better than 2nd place. On the first turn, don't hit the red/white striped barrier or you'll be DQd. You don't need to brake at all on the second turn just use the wall. The third turn is similar to the first. I slam the regular brakes to slow up a bit then tap the handbrake.
It took me about 2-3 hours of trying to get that lap time. I feel like it's mostly luck but I would also have several 54.X times in a row every now and again.
Hope this helps, good luck!
edit: Traction control 1 was probably the most important setting. Otherwise you will need to be really careful w/ accelerating because the comfort soft tires will just spin.